[xnor]

Nice.
 
This confirms what I've been saying, and also that frequency response is probably the most important aspect of (perceived) sound quality.
 
Okay, headphones are not perfectly minimum phase, but what is perfect in reality. After all, most headphones do not have any damping material at all. It's basically just a driver screwed into a plastic cup, so resonances are a given. But with some modding and EQing you can achieve pretty much any sound you want.

 

[vid]

Original AKG K 250:

 
MLS signal convolved with the K 250 inverse, lowpassed at 12 kHz (or 15, I forget) and fed into the K 250 again:

 
This time, unlike last time, the convolution filter was created from the same measurement session, i.e. positioning remained the same for both measurements (though the first graph above is from a different session - it's there for reference only).
 
I did a test where I convolved the impulse response of the non-convolved measurement - that one came out with a flat CSD except for some energy in the bass. The ridges only show up (or remain, since they're part of the natural response of those phones) when the convolution is fed through the phones.
 
Of course this brings up the question of what's flat. You need to measure the response before you can start convolving, meaning you'd need to have a measurement setup that's perfectly calibrated. You'd also need to play around with compensating the measurement that you create the convolution filter from - if you create it from a raw measurement that includes the HRTF, you'd end up with an incorrectly flat response. In that sense it might be easier to convolve one headphone to the response of another - at least in theory it shouldn't matter whether your measurements are absolutely correct or not as long as they produce the same result on repeated measurements, letting you see the difference in response between the two phones.

 

[arnaud]

Vid, this is neat. Also on the csd themselves, while I did not care much for the original layouts, the latest one are quite cool and useful. What software are you using for the recording and post-processing already? Also, you're using small mics at the entrance of ear canal or something else?

 

[vid]

Using stv014's MLS tone generator for the signal, GoldWave to record, HOLMImpulse to manipulate the recording/impulse response, a helper program I made to apply HRTF compensation to frequency responses exported to/from HOLM, and the command line version of Convolver (on SourceForge) for the convolving.
 
The mic is a small electret capsule at the end of a tube that's roughly 3 cm long and maybe about 7 mm wide (but in any case it has the measurements of an average ear canal). The other end of the tube is attached to a round disc (a few layers of thick cardboard with some bubble wrap in the middle and the outside covered with cotton cloth) to get a seal on headphones, and when desired, I attach an artificial ear (self-made, not very fancy) onto the disc. The system measures over-ear phones relatively accurately, but is more finicky with on-ears.

 

[ultrabike]

Thank you very much vid! What soundcard do you use to capture the response from the mic, and specifically what mic do you use. I have been looking at these two for a while:
 
Mic (seems to be a calibrated clone of the Behringer ECM8000):
http://www.parts-express.com/pe/showdetl.cfm?partnumber=390-801
 
Soundcard:
http://www.amazon.com/Focusrite-2i2-USB-Recording-Interface/dp/B005OZE9SA/ref=sr_1_1?ie=UTF8&qid=1350499302&sr=8-1&keywords=focusrite
 
Again. Thanks dude!

 

[vid]

The sound card is an Auzen Bravura and the mic is a no-name one that cost about $2.

 

[arnaud]

$2 for a mic, humm it probably comes with a calibration chart

 

[vid]

There are two ways you can go: spend money and get a calibration chart, or save money and suss out the response yourself - hoping that it's not too much out of whack to begin with.

 

[vid]

Smoothing via convolution?
 
Original K 250 (re-measured for comparison):

 
Convolved MLS signal fed into K 250:

 
This time the convolution filter was the relative difference between the original K 250 frequency response and the same K 250 frequency response but with 1/13 octave smoothing. Not sure why the ridges survived the convolution in the last test I did, but they didn't in this one.
 
I did a relatively quick ABX test on four random tracks between the original K 250 and the convolved K 250. In two songs I couldn't tell a difference, one was a bit shaky but ultimately couldn't tell them apart consistently, and one was relatively obvious. Good, because at least the filter didn't totally ruin the sound. Bad, because it didn't change it very audibly for the better either. Then again, the frequency response didn't change much - only the ringing was gone. (Although there needs to be a disclaimer here about the ringing in the treble. It's probably somewhat linked to ear canal resonances, whose exact frequency location depends on the listener's ear's physical attributes. Thus this convolution filter most possibly didn't hit the exact right spot for my ear to kill the ringing even though it did so for the measurement ear. But unlike in the treble, the ~5 kHz peak doesn't seem to change location due to ear anatomy, so no disclaimer for that one.)

 

[ultrabike]

That was an excellent test: smoothing the target curve to remove ringing. Your conclusions seem reasonable to me. Certain songs may mask the ringing while others would not. It probably also depend on the frequency where the ringing occurs. Like you suggested, there might also be person to person variation.
 
As far as your last test, if you are referring to post 858, notice that the ringing is quite a few dB bellow were it originally was.

 

[Joe Bloggs]

@vid if you want to smooth out the frequency response at your own ears you really want to EQ by your own ears.

http://www.head-fi.org/t/413900/how-to-equalize-your-headphones-a-tutorial
http://www.head-fi.org/t/615417/how-to-equalize-your-headphones-advanced-tutorial-in-progress

 

[vid]

The curious thing about convolution smoothing is that it seems to have eliminated ringing without altering the frequency response too much. Whether that offers a benefit, I don't know from just that one test - but I suspect it might be more difficult to imitate via manual EQing.
 
Here's two CSDs, the first is a raw measurement of the K 250 with the artificial ear attached, the second the same but without the ear (so just the ear canal tube):

 

 
The 4.5 or so kHz ridge stays in the same place, and to my eye so do the two treble ridges. The interesting property of measuring with the artifical ear and then without it is that the ear makes the 'ear canal' slightly longer, which in theory should lower the frequency of the ear canal resonances - and it can be seen (with some difficulty in these nonoptimal images) that the ~3 kHz peak shifted downwards when the ear was attached, same with the ~10 kHz peak. The ~3 kHz peak is for sure the first ear canal resonance, the ~10 kHz peak quite likely; in any case they both shift down in frequency while the other peaks remain the same, which is a good hint. But the point is that the two treble ridges (ringing) and their associated notches in the response don't seem to shift down in frequency, which might be a clue that they're not related to ear canal resonances (and I was kinda wondering why they would be in the first place).
 
Some simple tests of this can be derived by taking a smoothing convolution from one of the measurements and applying it to the other, which I'll do later.

 

[vid]

Had some tests and measurements. The sad thing is that the ringing notches move around just enough (usually about 50-100 Hz) between having the artificial ear in there and not that it makes things unreliable for fine-tuning.
 
The less sad thing is that I had a quick try at the mic-capsule-in-your-ear type of measurement method, and while it doesn't really work so well for a displayable frequency response, it should in theory position the ringing notches a bit closer to where they would be. As a general test, I measured the K 250 and the DT 990 in that way, created a convolution filter from their relative difference and fed it into the K 250. The result was that the K 250 came pretty close to the DT 990 in a listening test - closer than the more regular measurement method could. There were some issues in the treble, the sound wasn't an exact match, but I think with some work those issues could be solved.

 

[vid]

Mending a channel imbalance accurately via convolution.
 
Beyer DT 990, 1980s vintage. Different pads than in the last measurements I posted.
 
Measured channel balance, created an impulse response of the frequency difference, smoothed it out a bit, and applied it to the right channel.
 
Unconvolved, left/right:


 
Convolved, left/right:


 
Frequency response; unconvolved, left (orange)/right:

 
Convolved, left/right:

 
The CSDs don't show a large change, though the frequency graphs tell of a high degree of match between the left channel and the convolved right channel, whereas the original right channel is visibly off across the board (bear with the unreadable orange, I like the color).
 
The interesting thing about this is that I created the balancing filter by measuring the channel balance without an artificial ear, then applied that filter to the MLS signal when I measured the graphs with the artificial ear. In other words, adding an identical ear into both cups didn't change their relative channel balance. The earless filter filtered the eared measurements just fine - save for being a bit off around 10 kHz, which isn't bad. And this isn't a huge surprise. I've noticed before that a channel balance measurement taken without the artificial ear nonetheless corresponds well to the channel balance I hear with my own ears (though I'm speaking of half-open over-ear phones, mainly).

 

[ultrabike]

Awesome! Did you get the same balance correction filter when measuring with the artificial ear vs without the artificial ear? 
 
EDIT:
"...adding an identical ear into both cups didn't change their relative channel balance"
 
Sorry I think this is the answer to my question. This also suggests to me, that it may be best to compare plots of similarly measured headphones in relative terms together with one's own subjective experience of the headphone performance. That is, comparing plots across sites in absolute terms may be problematic given different acquisition methods and compensation.